The principal permeability tensor of inclined coalbeds during pore pressure depletion under uniaxial strain conditions: Developing a mathematical model, evaluating the influences of featured parameters, and upscaling for CBM recovery

摘要

In situ coalbeds are commonly inclined to one or multiple directions. The principal permeability tensor of an inclined coalbed may thus be non-coaxial to the uniaxial strain conditions, which are composed of two underlying assumptions: invariant vertical stress and confined horizontal boundaries. This paper developed a mathematical model to represent the principal permeability tensor of inclined coalbeds during pore pressure depletion under uniaxial strain conditions. This model adopted two geological properties to correlate the orientations of principal permeabilities and uniaxial strain conditions. One is the dip angle of inclined coalbeds, and the other is the pitch angle of cleats. The developed model was verified by field permeability data of the coalbeds in the San Juan Basin. Dip angle and pitch angle are the featured parameters of the developed model. This paper thus evaluated how the two angles influenced the magnitudes and evolution behaviors of principal permeabilities during pore pressure depletion under uniaxial strain conditions. The influences of dip angle and pitch angle on principal permeabilities can be attributed to their influences on the effective stresses normal to principal permeabilities. In order to upscale the principal permeability tensor for CBM recovery, this paper formulated a tensor-based index system for coal permeability evaluation. The tensor-based index system is composed of three indexes: the principal permeability tensor, the equivalent permeability tensors coaxial to engineering issues, and the geometric mean (GM) permeability of the three principal permeabilities. The principal permeability tensor can be used to optimize the pattern of vertical CBM wells, to determine the optimal directions of lateral wells, and to predict the propagating orientation of hydraulic fractures. The equivalent permeability tensors coaxial to engineering issues can be implemented into numerical simulators to improve the precision when evaluating and predicting the production performance of CBM wells. The GM permeability represents the ensemble transport capacity of coalbeds and can be used as an indicator to represent the productivity of coalbed reservoirs. This paper also preliminarily discussed how to use the tensor-based index system in CBM recovery.